4.7: GEO Patterns

Look at the cards below. Can you continue the pattern of circles, triangles and squares? Can you say how many circles, triangles and squares would be on cards 5, 6, and 10? In this section, we will practice finding patterns and extending them.

GEO Patterns

In order to continue patterns like the one with the shapes shown above, we can use the problem solving steps to help.

First, describe what you see.

Second, figure out what your job is. In these problems, your job will be to continue the pattern and describe cards 5, 6, and 10.

Third, make a plan. Decide how you will figure out and then continue the pattern.

Fourth, solve. Say how many circles, triangles and squares are on cards 5, 6, and 10.

Fifth, check. State the pattern you found and verify that it worked for all of the cards.

1. Look at the cards below. Continue the pattern of circles, triangles and squares. How many of each shape will be on card 5? Card 6? Card 10?

We can use the problem solving steps to help.

Describe: There are 6 cards. Cards 1-4 have circles, triangles and squares. Cards 5 and 6 are empty.

My Job: Figure out the pattern of circles, triangles and squares. Figure out how many of each shape are on cards 5, 6 and 10.

Plan: Count the number of circles on each card. Look for a pattern. Describe how many circles are on cards 5, 6 and 10. Count the number of triangles on each card. Look for a pattern. Describe how many triangles are on cards 5, 6 and 10. Count the number of squares on each card. Look for a pattern. Describe how many squares are on cards 5, 6 and 10.

Solve: Card 5 has 1 red circle next to 1 green triangle next to a stack of 5 blue squares. Card 6 has 1 red circle next to 1 green triangle next to a stack of 6 blue squares. Card 10 has 1 red circle, 1 green triangle, and 10 blue squares.

Check: There is always 1 red circle. There is always 1 green triangle. The number of blue squares is always the same as the card number.

2. Look at the cards below. Continue the pattern of circles, triangles and squares. How many of each shape will be on card 5? Card 6? Card 10?

We can use the problem solving steps to help.

Describe: There are 6 cards. Cards 1-4 have circles, triangles and squares. Cards 5 and 6 are empty.

My Job: Figure out the pattern of circles, triangles and squares. Figure out how many of each shape are on cards 5, 6 and 10.

Plan: Count the number of circles on each card. Look for a pattern. Describe how many circles are on cards 5, 6 and 10. Count the number of triangles on each card. Look for a pattern. Describe how many triangles are on cards 5, 6 and 10. Count the number of squares on each card. Look for a pattern. Describe how many squares are on cards 5, 6 and 10.

Solve: Card 5 has 1 red circle next to a stack of 6 green triangles next to a stack of 6 blue squares. Card 6 has 1 red circle next to a stack of 7 green triangles next to a stack of 7 blue squares. Card 10 has 1 red circle, 11 green triangles and 11 blue squares.

Check: There is always 1 red circle. The number of green triangles is always 1 more than the card number. The number of blue squares is always one more than the card number.

3. Look at the cards below. Continue the pattern of circles, triangles and squares. How many of each shape will be on card 5? Card 6? Card 10?

We can use the problem solving steps to help.

Describe: There are 6 cards. Cards 1-4 have circles, triangles and squares. Cards 5 and 6 are empty.

My Job: Figure out the pattern of circles, triangles and squares. Figure out how many of each shape are on cards 5, 6 and 10.

Plan: Count the number of circles on each card. Look for a pattern. Describe how many circles are on cards 5, 6 and 10. Count the number of triangles on each card. Look for a pattern. Describe how many triangles are on cards 5, 6 and 10. Count the number of squares on each card. Look for a pattern. Describe how many squares are on cards 5, 6 and 10.

Check: The number of red circles is always one less than the card number. There is always 2 green triangles. The number of blues squares is always twice the card number.

Earlier Problem Revisited

We can use the problem solving steps to help.

Describe: There are 6 cards. Cards 1-4 have circles, triangles and squares. Cards 5 and 6 are empty.

My Job: Figure out the pattern of circles, triangles and squares. Figure out how many of each shape are on cards 5, 6 and 10.

Plan: Count the number of circles on each card. Look for a pattern. Describe how many circles are on cards 5, 6 and 10. Count the number of triangles on each card. Look for a pattern. Describe how many triangles are on cards 5, 6 and 10. Count the number of squares on each card. Look for a pattern. Describe how many squares are on cards 5, 6 and 10.

Solve: Card 5 has one red circle next to a stack of 5 green triangles next to a stack of 7 blue squares. Card 6 has one red circle next to a stack of 6 green triangles, next to a stack of 8 blue squares. Card 10 has one red circle, 10 green triangles, and 12 blue squares.

Check: There is always 1 red circle. The number of green triangles is the same as the card number. The number of blue squares is always two more than the card number.

Vocabulary

One type of pattern is when the number of a certain object increases, decreases, or stays the same in a consistent way. In this concept, we saw patterns of triangles, circles and rectangles. With any pattern you should be able to describe the pattern and how to get from one step of the pattern to the next.

Examples

Example 1

Continue the pattern of circles, triangles and squares. How many of each shape will be on card 5? Card 6?